VBTutorial2

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VB applications on PI systems

To the Tutors

Sason remarks and prospective 2 hours talk +

Philippe's remark on the initially proposed tutorial. are included in bold.

Qualitative

• Exercices from The Book ... >PCH< (30')

Computational

• Allyl cation : VB 3 configuration (3rd configuration has a large weight).
• Benzene : question about basis of covelent structures (paper exercise, then xmvb zith str=cov), then all ionics.
• Ozone : paper exercise ; expand MO wf in VB basis, wieghts of biradical with HF, compute with XMVB (VBSCF, BOVB)
• Benzyl radical with most spin alternant determinants (2 determinants) (p228 of The Book) show spin location. Objection : this uses Heisenberg spin hamiltonian theory, a topic that we do not teach.

(trash: * O2 paradigm : compute singlet - triplet gap : too hard

• H2O lone pairs : compute H2O+ states (2 configurations mixing) Objection : did you try to do that ? If we let the orbitals optimize themselves, I guess we will converge to the MO solution with weight 1.0, the other structure with weigt 0.0. The H2O+ states would better be done as qualitative exercises.)

Exercices

Remark : in all the following exercises, <math>\pi</math> the system will be taken as active, and the <math>\sigma</math> system as inactive. In all VB calculations, the <math>\sigma</math> orbitals shall be described by MOs delocalized onto the whole molecule.

Exercise 1 : The allyl radical and cation

1. Structures of the allyl radical :
   1. What are the three possible covalent structures for the allyl radical molecule ? Use qualitative VB theory to compute their energy, and show that two of them are degenerate.
   2. Show that the third structure can be expressed as a linear combination of the first two structures, and thus that only two of the three covalent structures form a complete basis of non-redundant structures (Rumer basis).
   3. What are the possible ionic structures for the allyl radical ? Based on your chemical knowledge, propose a selection subset of the most chemically meaningful covalent + ionic structures.
2. Structures of the allyl cation, and weights from Hückel theory :
   1. Use Rumer's rules to find a complete basis of covalent structures for the allyl cation.
   2. What are the possible ionic structures for the allyl cation ? Based on your chemical knowledge, propose a selection subset of the most chemically meaningful covalent + ionic structures.
   3. Use the HuLis software to retrieve the Hückel MOs for allyl cation. Write a single-determinant MO wave function based on Hückel orbitals. Develop it into the basis of atomic orbitals, to get an expression in terms of VB structures. Compute by hand the weights of the different structures (neglecting all overlaps for simplicity).
3. Allyl radical and cation weights :
   1. Compute a VBSCF wave function for allyl radical (6-31G* basis set) using your selected set of structures (questions 1.3 and 2.2). Compute a VBSCF wave function including the complete set of VB structures, using the "str=all" keyword. Compare the weights and energies for both wave functions to validate your selection of structures.
   2. Compute for allyl radical a BOVB wave function which include only your selected set of most chemically meaningful structures (use the guess orbitals obtained at the VBSCF level). Compare the weights obtained at the VBSCF and BOVB level.
   3. Repeat questions 3.1 and 3.2 for the allyl ion. Compare the BOVB weights to the weights predicted by simple MO theory.
4. Resonance energies :
   1. We want to build a wave-function corresponding to only one Lewis structures for the allyl radical. To do so, we will include in the wave-function only one covalent structure, and the ionic structures associated to this covalent bond. Propose a selection of VB structures which would describe one Lewis structure for the allyl radical.
   2. Compute this wave function at VBSCF then BOVB levels. Deduce what is the resonance energy of the allyl radical at the BOVB level.
   3. Repeat questions 4.1 and 4.2 for the allyl cation.

>> Answer

Exercise 2 : Radical character of ozone

1. Paper exercice :
   1. Propose a complete basis of non-redondant VB structures for the ozone molecule. Based on your chemical knowledge, propose a selection subset of the most chemically meaningful structures.
   2. Use the HuLis software to retrieve the Hückel MOs for ozone. Write a single-determinant MO wave function based on Hückel orbitals. Develop it into the basis of atomic orbitals, to get an expression in terms of VB structures.
   3. Compute by hand the weights of the different structures (neglecting all overlaps for simplicity). What is the radical character of ozone according to simple MO theory ?
2. Computer exercise :
   1. Compute a VBSCF wave function for ozone (6-31G* basis set) using your selected set of structures (question 1.1). Compute a VBSCF wave function including the complete set of VB structures, using the "str=all" keyword. Compare the weights and energies for both wave functions to validate your selection of structures.
   2. Compute a BOVB wave function for ozone which include only your selected set of most chemically meaningful structures (use the guess orbitals obtained at the VBSCF level).
   3. Compare the weights obtained at the VBSCF and BOVB level. Compare the BOVB diradical weight to the value predicted by simple MO theory.

>> Answer

Exercise 3 : Resonance energy of Benzene

To be written...